Question: Solve for $x$ and $y$ using elimination. $\begin{align*}7x-y &= -2 \\ -5x+y &= -2\end{align*}$
Solution: We can eliminate $y$ when its corresponding coefficients are negative inverses. Add the top and bottom equations. $2x = -4$ Divide both sides by $2$ and reduce as necessary. $x = -2$ Substitute $-2$ for $x$ in the top equation. $7( -2)-y = -2$ $-14-y = -2$ $-y = 12$ $y = -12$ The solution is $\enspace x = -2, \enspace y = -12$.